Find Amplitude, Period, and Phase Shift y=2sin(4x)

Problem

y=2*sin(4*x)

Solution

1. Identify the standard form of the sine function, which is y=A*sin(B*(x−C))+D

2. Determine the amplitude by taking the absolute value of the coefficient A

|A|=|2|

Amplitude=2

3. Calculate the period using the formula (2*π)/|B| where B=4

Period=(2*π)/4

Period=π/2

4. Find the phase shift by identifying the horizontal displacement C Since there is no value subtracted from x inside the function, C=0

Phase Shift=0

Final Answer

Amplitude=2,Period=π/2,Phase Shift=0

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